A ray-shooting approach is presented for calculating the interior radar cross section (RCS) from a partially open cavity. In the problem considered, a dense grid of rays is launched into the cavity through the opening. The rays bounce from the cavity walls based on the laws of geometrical optics and eventually exit the cavity via the aperture. The ray-bouncing method is based on tracking a large number of rays launched into the cavity through the opening and determining the geometrical optics field associated with each ray by taking into consideration: (1) the geometrical divergence factor, (2) polarization, and (3) material loading of the cavity walls. A physical optics scheme is then applied to compute the backscattered field from the exit rays. This method is so simple in concept that there is virtually no restriction on the shape or material loading of the cavity. Numerical results obtained by this method are compared with those for the modal analysis for a circular cylinder terminated by a PEC plate. RCS results for an S-bend circular cylinder generated on the Cray X-MP supercomputer show significant RCS reduction. Some of the limitations and possible extensions of this technique are discussed. >

Shooting and bouncing rays: calculating the RCS of an arbitrarily shaped cavity

Techniques based on the method of modal expansions, the Rayleigh-Stevenson expansion in inverse powers of the wavelength, and also the method of moments solution of integral equations are essentially restricted to the analysis of electromagnetic radiating structures which are small in terms of the wavelength. It therefore becomes necessary to employ approximations based on “high-frequency techniques” for performing an efficient analysis of electromagnetic radiating systems that are large in terms of the wavelength.

Techniques for High-Frequency Problems

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Mutual Coupling Considerations in the Development of Multi-feed Antenna Systems

The physical optics approximation is employed to derive the radiation integral for a doubly curved offset reflector antenna illuminated by an arbitrary source. A novel procedure is presented for expressing the radiation integral in terms of a summation of Fourier transforms of an "effective" aperture distribution which includes the effect of the curvature of the surface. The Jacobi-Bessel series is used to evaluate the Fourier transforms. The vector nature of the far-field pattern is studied by evaluating its three Cartesian components in a unified fashion. The rapid numerical evaluations of the expressions obtained are demonstrated via extensive test cases. In particular, the scattering characteristics of symmetric and offset parabolic, spherical, and shaped reflectors are studied in detail, and comparisons are made with other available data.

Shaped reflector antenna analysis using the Jacobi-Bessel series. [design for space and satellite communication]

Shaped reflector antenna analysis using the Jacobi-Bessel series

The high-frequency asymptotic solution of diffraction by a conducting subreflector is studied. By using Keller's geometrical theory of diffraction and the newly developed uniform asymptotic theory of diffraction, the scattered field is determined up to an including terms of order k^{-1/2} relative to the incident field. The key feature of the present work is that the surface of the subreflector is completely arbitrary. In fact, it is only necessary to specify the surface at a set of discrete points over a random net. Our computer program will fit those points by cubic spline functions and calculate the necessary geometrical parameters of the subreflector. In a companion paper by Y. Rahmat-Samii, R. Mittra, and V. Galindo-Israel, the scattered field from the submflector is used to calculate the secondary pattern of an arbitrarily shaped reflector by a series expansion method. Thus, in these two papers, it is hoped that we have developed a "universal" computer program that can analyze most dual-reflector antennas currently conceivable. It should also be added that our method of calculation is extremely numerically efficient. In many cases, it is one order of magnitude faster than the conventional integration method based on physical optics.

Diffraction by an arbitrary subreflector: GTD solution

The radiation pattern of a feed element is approximately described by a simple function (\cos \theta)^{q} . For a given element spacing of the feed array, we give simple formulas for estimating the practical value of q when the element is an open-ended rectangular waveguide, an open-ended circular waveguide, a pyramidal horn, or a cigar antenna.

Realizable feed-element patterns for multibeam reflector antenna analysis

For a given source and observation point, specular points on a conducting surface must be found in order to apply the geometrical optics theory to calculate the reflected field. An efficient method is presented for finding all the specular points for the special case in which the conducting surface is a part of a surface of revolution. Our method, which reduces the conventional two-dimensional search to a one-dimensional search, results in a significant savings in computer time. A one-dimensional search also makes it economically feasible to obtain a global solution for certain classes of surface, source, and observation point geometries that do not render solutions in the more conventional two-dimensional searches.

P. Cramer

Papers

Diffraction by an arbitrary subreflector: GTD solution

Realizable feed-element patterns for multibeam reflector antenna analysis

Determination of specular points on a surface of revolution